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Analysis of mica spaced Fabry-Perot filters

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#1 ch-viladrich

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Posted 10 January 2015 - 06:51 AM

Dear All,

Further to this very interesting post on etalon basics :http://www.cloudynig...-etalon-basics/

and given the ongoing bad weather down here, I tried to carry out some analysis of the performances of mica-spaced Fabry-Perot interference filters (in other words Daystar or Solar Spectrum filters) :

 

http://www.astrosurf...nt/solar/FP.htm

 

My point was to check :

 

1) What is the impact of F/D ratio on the bandpass of the filter ?

 

For example, calculations show that a 0.3 A filter used at F/20 would have an effective band pass of 0.85 A.

2) What is the impact of the tilt of the filter on the band pass ?
Indeed, some keen eye observers do have notice that poor focuser would lead to reduced image contrast.
The reason why is that the filter should be square to the optical axis, otherwise the band pass  broadens .
As an example, a 1° tilt of the filter would turn a 0.3 A filter into a 0.5 A filter.

 

PS: do not hesitate if you notice any flaw in the formulae used in these calculations ...

 

Best regards

Christian Viladrich

Attached Thumbnails

  • FWHM-N.JPG

Edited by nitegeezer, 18 January 2015 - 06:11 PM.
Graph removed as requested


#2 BYoesle

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Posted 10 January 2015 - 08:58 AM

BRAVO! :bow:   Excellent analysis Christian  :waytogo:

 

I note that similar bandpass broadening can occur if the telecentric lens system is not optimized to the objective focal length -- as you have cited -- and is at least partly why DayStar rightly does not specify a bandpass for the Quark.  This too will be more significant the narrower the bandpass of the filter.


Edited by BYoesle, 10 January 2015 - 09:29 AM.


#3 marktownley

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Posted 11 January 2015 - 03:27 PM

A great analysis Christian, i've noticed these effects with my Quark.



#4 George9

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Posted 12 January 2015 - 08:52 PM

Very nice! George



#5 BYoesle

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Posted 13 January 2015 - 01:06 AM

 

PS: do not hesitate if you notice any flaw in the formulae used in these calculations ...

 

Christian:  I noticed that none of the filters reach their specified FWHM at the commonly accepted focal ratio of F30, especially the 0.3 A filter...  This is a confirmation of the comments of Mark Wagner in the Etalon Basics thread, so I think your formulas likely are spot-on.

 

 

 

To get narrower or even to .3Ang you really need to be at F/45 or higher depending on the HW of the etalon in an telecentric beam. If you use a collimated system, then the (sweet spot) will be only a small area in the center at these narrower HW etalons.
If you are using a barlow or telecentric or just stopping down the scope you will never get narrower then .3Ang regardless the HW of the etalon if you are faster then F/35.

 

It is also interesting to note that the on-band tilt performance - and therefore the etalon acceptance angle - is very similar for all three band-passes chosen for study (~ 0.5 degree).  I would have erroneously assumed that a narrower FWHM filter would have a proportionally smaller acceptance angle.  What is instead demonstrated is that the the amount of degradation from tilt as a fraction of the band-pass is greater the narrower band-pass -- e.g. there is a greater sensitivity to tilt.  Hmmm...


Edited by BYoesle, 13 January 2015 - 01:21 AM.


#6 George9

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Posted 13 January 2015 - 08:46 AM

 

Christian:  I noticed that none of the filters reach their specified FWHM at the commonly accepted focal ratio of F30, especially the 0.3 A filter...  This is a confirmation of the comments of Mark Wagner in the Etalon Basics thread, so I think your formulas likely are spot-on.

 

 

How are filters specified when they are sold? 0.3A at F30 or at a theoretical F-infinity? If they determine the bandwidth visually, then it might be specified at F30. Or perhaps they just know what a 0.3A (at infinity) looks like at F30 and call it from experience. George



#7 BYoesle

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Posted 13 January 2015 - 03:02 PM

Hi George,

 

I believe the specified band-pass is the theoretical (e.g. focal ratio approaches infinity) specification, and is determined by a laboratory spectrometer.

 

Real-world performance will be determined by the instrument angles (i.e. focal ratio) and field angles.  For these types of filters, the instrument angles are generally a straightforward extrapolation from the focal ratio.  The field angles (and tilted instrument angles) depend on the auxiliary optics such as the telecentric lens specifications in conjunction with the objective focal length.  

 

 

i've noticed these effects with my Quark.

 

While DayStar states the the Quark uses a "truly telecentric" barlow lens (as opposed to a Powermate?)  - http://www.daystarfi.../QuarkFlyer.pdf  - the only way the "truly telecentric" performance could be realized is if DayStar specified the focal length of the objective the telecentric was designed to be used with.  And for the Quark there is also another set of variables - the original FWHM spec. of the etalon and the filter grade used.  http://www.daystarfilters.com/Quark/QuarkUniformity 

 

It would perhaps be better if the manufactures supplied a standard specification scheme as you are suggesting, such as the band-pass when used at a native (e.g. non-amplification) focal ratios -- i.e. f15, f20, f30, f45, etc.  Thanks to Christian, we have values for three specific "laboratory" band-passes, and one can interpolate for other band-passes at commonly available focal ratios.  Note these curves are for the native focal ratio of an objective without amplification, and would be further impacted by the use of standard barlow lenses, un-optimized correctors such as Powermate barlows, or the Baader telecentric lenses used at focal lengths other than the 800 mm for which they were originally designed.


Edited by BYoesle, 13 January 2015 - 05:47 PM.


#8 ch-viladrich

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Posted 14 January 2015 - 02:42 PM

Thanks to all :-)

 

Just a word of cautious here : the formula for the FWHM as function of F/D ratio is OK for sure. Still, I am not 100% sure of the fomula giving the relation between the FWHM and the tilt. I am going to check with people who know more about F-B.

 

What I would like to do in a following step, is to check the evolution of the bandpass at 10% transmission as a function of F/D.

As explained in the very interesting thread on "etalon basics", the band pass at 10% transmission of a one-cavity F-P is between 2.5 to 3 X the band pass at 50% transmission. This bandpass at 10% transmission is partly "responsable" of the contrast we have between the chromosphere and the photosphere. The main function of double stacking is not to reduce the FWHM, but to reduce the band pass at 10% transmission, ie to have a transmisson profile with steeper wings.

 

It's fun to have a look at these questions :-)



#9 pbsastro

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Posted 15 January 2015 - 03:27 AM

Christian:  I noticed that none of the filters reach their specified FWHM at the commonly accepted focal ratio of F30, especially the 0.3 A filter...  This is a confirmation of the comments of Mark Wagner in the Etalon Basics thread, so I think your formulas likely are spot-on.

 
How are filters specified when they are sold? 0.3A at F30 or at a theoretical F-infinity? If they determine the bandwidth visually, then it might be specified at F30. Or perhaps they just know what a 0.3A (at infinity) looks like at F30 and call it from experience. George


I think SolarSpectrum rates the filters at f/40. From Mark:
"
A .2Ang filter(F/40) will be about .36Ang at F/32 but at F/50 it will be about .15Ang.
Where a .3Ang (F/40) will be about .39ang at F/32 but at F/50 it will be about .27ang
You take a .7Ang filter (F/40) it will be .73ang at F/32 and .65ang at F/50.
"

#10 marktownley

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Posted 15 January 2015 - 03:17 PM

It's fun to have a look at these questions :-)

 

I completely agree! :)



#11 ch-viladrich

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Posted 16 January 2015 - 03:41 AM

Hi,

 

I added the curve of FWHM = f(F/D) for the 0.4 A filter and expand the figure to F/D = 50 :

 

http://www.astrosurf...olar/FWHM-N.JPG



#12 BYoesle

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Posted 16 January 2015 - 12:59 PM

:waytogo:

 

Thank you Christian.

 

Could you do another plot that would be very informative?

 

It would be nice to have a comparison graph of the band-pass performance changes that occur for an air-spaced etalon(s) with tilt, since this is the most common method for tuning a front etalon, and is sometimes used for internal etalons.  It is said that air spaced etalons are more sensitive due to the lower refractive index of the gap material, and it would be nice to know how much more sensitive to tilt they are in comparison to the 0.3, 0.5, and 0.6 mica etalons you have already plotted.

 

Thanks again.


Edited by BYoesle, 17 January 2015 - 09:28 AM.


#13 ch-viladrich

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Posted 17 January 2015 - 09:28 AM

Hi,

 

Here are some news ...

First of all, I made a big mistake on the influence of the tilt on FWHM : in a collimated beam, the tilt does not change the FWHM (nor the shape of the transmission curve). Sorry for this mistake  : - (

 

Finally, I use the formulae of the F-P to build up a model of the Daystar Ha transmission profile based on the data provided in Daystar white book. It fits very nicely with the measurements of a 0.3 A Daystar made at the solar tower of Meudon observatory.

The results are shown here :

http://www.astrosurf.../FP-Daystar.htm

 

Here is, among various things, the comparison between a 0.6 A filter, double stacked 0.6 filters, and 0.38 A filter :

http://www.astrosurf...ouble-stack.JPG

 

An other interesting thing : the bandwidth at 10% transmission is equal to three times the FWHM, which fits very nicely with the measurements made at Meudon solar tower.

The entry page for all of this is there :

http://www.astrosurf...nt/solar/FP.htm

Attached Thumbnails

  • Daystar-double-stack.JPG
  • Daystar-tilt.JPG

Edited by ch-viladrich, 17 January 2015 - 09:40 AM.


#14 ch-viladrich

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Posted 17 January 2015 - 09:31 AM

BTW, how to remove my faulty graph about FWHM = f(tilt) ?



#15 BYoesle

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Posted 17 January 2015 - 11:01 AM

:bow:  :bow:  :bow:

 

Outstanding graphs and valuable information not easily found anywhere else Christian -- bookmarked and saved!

 

I note particularly that the double stacked filter system not only has a  reduced FWHM band-pass, equivalent to a more expensive filter, but even greater suppression of the transmission "tails" for even better contrast performance than the equivalent single filter.  George 9 determined that two ideal 0.7 Angstrom filters have a FWHM of 0.45 A, and similarly reduced transmission tails:

 

stacked etalon curves.jpg

 

Again, thank you very much  :jump:



#16 BYoesle

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Posted 17 January 2015 - 11:08 AM

 

First of all, I made a big mistake on the influence of the tilt on FWHM : in a collimated beam, the tilt does not change the FWHM (nor the shape of the transmission curve). Sorry for this mistake 

 

Hmm... are you sure it's a mistake?  Could it be that in a collimated system tilt only results in a center wavelenght shift, whereas in a telecentric system you get the band-pass broadening (in addition to a CW shift)?  I know that I have seen references to tilt-induced band-pass broadening and CW (tuning) shifts for both types of systems, but perhaps that is a carry-over form just the telecentric based systems erroneously assumed to occur for collimated systems as well?


Edited by BYoesle, 17 January 2015 - 11:25 AM.


#17 BYoesle

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Posted 17 January 2015 - 11:40 AM

Oooops!  Nevermind - I see you already answered this:

 

 

In a non collimated beam (ie. if the incoming beam was a cone of light), such as with a Barlow lens or a telecentric system, the tilt of the axis of the incoming cone of light would widen the FWHM (more to come on this latter on ...).

 

Another "fly in the ointment" however is how well the two types of systems (collimated verses telecentric) deal with field angles in air spaced verses solid spaced (mica) etalons.

 

Again, fantastic information Christian!



#18 ch-viladrich

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Posted 17 January 2015 - 11:48 AM

Yes and no ;)

 

All of this comes from the change in CWL with the tilt of the incident beam :

 

1- If the incident beam is collimated  (parallel beam of light ):

We only have a shift in wavelenght :

http://www.astrosurf...r/CWL-tilt1.JPG

 

The FWHM broadening is really negligeable (10-5 in relative value for one degree tilt).

The formula is here :

http://www.astrosurf...r/formula-3.JPG

 

What is interesting is that the tilt does not change the transmission profile.

 

2- If the incident beam is a cone of light (which is what we have in our telecope) :

a) The best we can do is to use a telecentric system:

The incident cones of light have the same geometry all over the field of view.

As you said, the integration of the shift of CWL for all the angles within the cone of light, convoluted by the FWHM of the filter, results in a FWHM broadening (that one is a long sentence ;) )

 

b) if we do not have a telecentric system :

the angle of the cones of light are set by the F/D ratio (=> FWHM broadening), but the angle of the axis of the cone of light changes along the field of view => CWL shift along the field of view. It seems that the second effect add an additional FWHM broadening depending of the position in the field of view. I still have to work on that ;)



#19 BYoesle

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Posted 17 January 2015 - 03:41 PM

Hi Christian,

 

 

If the incident beam is collimated  (parallel beam of light )... The FWHM broadening is really negligeable (10-5 in relative value for one degree tilt)... 

if we do not have a telecentric system :
the angle of the cones of light are set by the F/D ratio (=> FWHM broadening), but the angle of the axis of the cone of light changes along the field of view => CWL shift along the field of view. It seems that the second effect add an additional FWHM broadening depending of the position in the field of view. I still have to work on that ;)

  

 

Hmm... good food for thought.  However, it does remind me of and make me wonder if the "sweet spot" found in collimator based systems is due to only CWL/band-pass shifting, or if band-pass broadening also might be at work, and what that would look like...  So thinking out loud so to speak:

 

If we examine the curves you have given for the 0.6 A filter in a collimated beam, it appears we also might encounter band-pass broadening due to field angle magnification.  For example, if the collimator focal length is 1/4 the objectives FL, we will have a field angle magnification of 4 x, and the sun's limb field angle will be 0.25 x 4 = 1 degree.  We can see in this system the FWHM is blue-shifted by ~ 0.4 A at the limb, with an identical 0.4 A shift at the 10% transmission.

 

Daystar-tilt field angle.jpg

 

Could "integration of the shift of CWL" of the field angles in the collimator system be contributors to band-pass broadening - just as the suspected broadening that occurs with a telecentric based system are due to the non-normal angles of the F/D light cones?  The answer indeed is no, at least for the filter diameter as a whole.  This broadening would be the FWHM from the right side of the blue transmission curve to the left side of the green transmission curve or beyond.  We would see the decrease in disc contrast due to increased continuum light, but prominences would not be affected, or perhaps become even brighter due to blue Dopper shifiting events.  So if prominences remain visible, this would indicate the band-pass was broadened due to the wider band-pass still encompassing the H alpha emission line.

 

But what we observe for disk features is that more light from the photosphere intrudes and decreases contrast, but for prominences away from the suns disc, the off-axis CWL shift results in the filter eventually going off-band, and prominences disappearing (i.e. the green transmission curve).  This is also why minimizing field angle magnification is important in collimator based systems for good overall band-pass/contrast performance.  

 

The differences between collimator verses telecentric systems:  OPTIMIZED telecentrics will have a uniform broadening of the filter band-pass across the etalon due to all light cones (e.g. center and limb) having the same intercept angles at the etalon.  This broadening is apparently due only to the F/D angles of the light cone -- with the narrower the F/D cone allowing the tighter the band-pass, and why optimizing the F/D ratio is so important the narrower the filter bandpass.  Collimator systems are inherently non-uniform in CWL shifting, which is highly dependent on field angle magnifications off-axis presented to the etalon.

 

However, if we use a non-optimized telecentric system - e.g. a typical barlow, "telecentric barlow," or a proper telecentric used with an incorrect focal length - we might likely get both FWHM broadening and CWL shifting across the etalon, e.g. resulting in a "sweet spot" due to "cone tilt."   This again is what I have observed.  But of course I could be wrong in my thought analysis...

 

_________________________________________________

 

Addendum:  Going back and reviewing the thorough treatise on telecentric performance by Gene Baraff ( http://home.comcast....erving/Tele.pdf ):

 

In the less-than-ideal situation where design and actual focal lengths differ, the cone axes are tilted. That tilt gives rise to wavelength shift [Equation (21)] and to pass-band broadening [Equation (22)], both of which become worse with distance from the axis...  Emphasis added.

 

Note that in Figure 4 (pg. 18) the cone tilts vary non-linearly with distance from the optical axis, just as CWL shifts do in a collimator based system (seen in your plot of tilt angles):

 

The shift - towards shorter wavelengths - grows quadratically with distance from the axis.  In addition to the shift, there is broadening because of the range of angles striking a given image point.

 

From Gene's work, it indeed appears that for an un-optimized telecentric system, CWL shift (generating a "sweet spot") is the dominant consequence, with band-pass (and transmission profile) broadening seemingly of secondary significance in the majority of instances, provided the overall F/D ratio is already optimized.


Edited by BYoesle, 19 January 2015 - 08:32 AM.


#20 ch-viladrich

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Posted 25 January 2015 - 12:15 PM

Hi Bob,

Finally, I went through the equations given for a perfect F-P in the excellent book on thin-film optical filter by Macleod (thank Bob71741 for the link !)

If I am not misleaded, the basic and only factor at work is the change of CWL with incidence of light. This explains the broadening of FWHM in a telecentric system when F/D ratio decreases (associated to the shift of CWL).

This also explains the broadening of FWHM (associated to the shift of CWL) in a no telecentric system due to the combination of field angle and cone angle.

I'll try and add some new graphs on this very soon.



#21 marktownley

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Posted 27 January 2015 - 04:42 PM

great work Christian, thanks!



#22 ch-viladrich

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Posted 28 January 2015 - 09:14 AM

Thanks Mark :-)

 

Still working on it. I made some updates to the web page (drawings, formulae, figures) :

http://www.astrosurf...nt/solar/FP.htm

 

For example, here is a figure giving the FWHM broadening for three mica-spaced F-P etalons (0.6 A, 0.5 A, 0.4A FWHM) according to the F/D ratio and to the field angle. Remember the field angle is the angle between the axis of the incoming cones of light and the perpendicular of the F-P. In a telecentric system this angle is equal to 0. In non telecentric systems (or in non optimised telecentric systems) this "field angle" depends on the distance from the optical axis.

 

FWHM-field-angle.JPG



#23 BYoesle

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Posted 28 January 2015 - 09:32 AM

:waytogo:    Most interesting and very useful information!  Thank you very much Christian. 



#24 pbsastro

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Posted 03 February 2015 - 02:36 PM

Christian,
Thank you for your work.

You say "the transmission profile is steeper with a bandwidth at 10% equal to 2.3 FWHM (instead of 3 FWHM)"

However from your graph it looks the difference will be even bigger at 3% or 1%. So the more important double stack will be.

You also say: "An other way to cut down these transmission wings, could be to stack a 1.5 A FWHM filter on top of the Daystar filter (tests are ongoing ...)"

Any updates on this? I am considering that my self. That is a 0.3A SolarSpectrum (about 0.38A at f/34) with a 0.7A airspaced (about 1.2A at f/34).
Any chance you could simulate this 0.38A+1.2A (or 1.5A) to get the 10% and 3% or 1% FWHM?

Thanks,
Pedro

Edited by pbsastro, 03 February 2015 - 02:38 PM.


#25 bob71741

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Posted 03 February 2015 - 07:10 PM

Pedro

For the 0.3Å & 0.7Å filters the FWHM=0.26Å; the 10% BW= 0.63Å; and the 1% BW= 1.35Å

For the 0.38Å & 1.2Å filters the FWHM=0.35Å; the 10% BW=0.89Å; and the 1% BW=1.95Å

For the 0.38Å & 1.5Å filters the FWHM=0.36Å; the 10% BW=0.94Å; and the 1% BW=2.14Å

 

The skirt ratios (with respect to FWHM) for the above filter pairings are:

2.43(10%) & 5.17(1%) for the 0.3Å & 0.7Å

2.55(10%) & 5.57(1%) for the 0.38Å & 1.2Å

2.63(10%) & 5.97(1%) for the 0.38Å & 1.5Å

 

Remember that for a single stack the 10% ratio is 3 and the 1% ratio is 9.95

for a double stack etalon of the same FWHM the 10% ratio is 1.47 and the 1% ratio is 3




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